Finite Group DatabasebetaFinite Group Databasebeta| order | 3700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C25×C37 ⋊ C4 |
| Sylow | C37 ⋊ #1035 |
| Sylow | C25 ⋊ #3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C37 | C4 |
| Frattini | C5 | #10625191 |
| socle | C5×C37 | AGL(1,𝔽5) |
| prime radical, cosocle | D925 | C2 |
| LCS | G ▷ C25×C37 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 925 |
Polycyclic presentation:
2^2,5,37,5|a^2=b,c^5=e,c^a=c^2e,d^a=d^31,e^a=e^2,c^b=c^4e^4,d^b=d^36,e^b=e^4235 conjugacy classes — view the full character table.
| maximal subgroup of | #16814854⋊C3, C3×#16814854, C3⋊#16814854, … |
| maximal normal subgroup of | #16814854⋊C3, C3×#16814854, C7×#16814854 |
| maximal quotient of | C3×#16814854, C3⋊#16814854, C7×#16814854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3700, 8);